4119
being augmented by " and (p')1 2, we obtain the transition energies 4.62, 2.14, and 0.64 eV for CF2, FCH, and CH2 and the results labeled Cl in Figures 9-11 and Tables I—III. While we are encouraged by the agreement with experiment, we consider it somewhat fortuitous since it is quite likely that the correlation energy loss upon dissolution of the 2 lone pair is greater32 than the 0.25 eV we find from the minimal Cl. D. Singlet-Triplet Transition. In going from the sBi state of CF2 or CH2 to the corresponding 4Bi state we neither disrupt any existing nor form any new electron pairs and we therefore expect the correlation energy in these two states to be comparable. Consequently, we anticipate that the energy difference 3A" should be adequately repre3Bi or 1A" 4Bi sented by the various Cl functions we have described. To the extent that this is true we note that the reliability of our 1Ai-3B1 or 1A'-3A" separations may be estimated by observing how well we account for the various singlet-singlet transitions. Since we do very well in estimating this transition in CF2 (4Bi *- *Ai) and FCH 4A') (see Table IV), we expect the singlet(‘A" triplet separations to be accurate, so in CF2 we predict that the 3Bi is 39 kcal above the ‘Ai state, while in FCH the ' and 3A" are separated by a very small (~0 kcal) energy. Also, since our computed energy for the
J. Am. Chem. Soc. 1971.93:4119-4125. Downloaded from pubs.acs.org by KAOHSIUNG MEDICAL UNIV on 07/02/18. For personal use only.
—
—
(32) Indeed E. A. Scarzafava, Ph.D. Thesis, Indiana University, 1969, estimates the correlation energy in an oxygen lone pair in the water molecule as approximately 1 eV.
A'Bi
X4Ai transition in CH2 is too low by 5 kcal expect the 3Bi to be 19 kcal below the ‘Ai state even though our raw data predict this separation to be 24 kcal. Our estimate is in disagreement with recent experimental results33 which indicate a separation of 1-2 kcal, and on the basis of the above arguments this would imply an error of 18 kcal in the 1Bi-3B1 separation, which seems unreasonable. However, since this discrepancy must be resolved, we are undertaking a detailed study of the correlation energy contribution to the various states of CH2 and will report the results as soon *-
we
as possible.34
Acknowledgment. The contour plots were constructed with routines written by Dr. Vincent Nicely, and it is a pleasure to acknowledge their use. (33) R. W. Carr, Jr., T. W. Eder, and M. G. Topor, J. Chem. Phys., 53, 4716 (1970). (34) Note Added in Proof. Recently, O'Neil, Schaefer, and Bender, manuscript in preparation, have used the iterative natural orbital technique [C. F. Bender and E. R. Davidson, J. Phys. Chem., 70, 2675 (1966)] to construct wave functions for various states of CHj. Using Huzinaga's (9s5p/4s) basis [(S. Huzinaga, J. Chem. Phys., 42, 1293 (1965)] contracted to [4s2p/2s] as recommended by Dunning [T. H. Dunning, Jr., J. Chem. Phys., 53, 2823 (1970)], a 298 and a 408 configuration representation of the lAi and 3Bi states, respectively, were
constructed as a function of geometry. Their result for the 3Bi-1Ai -0.96 eV (-22 kcal), is £pAi (104.4°)] splitting, £[3Bi (133.3°)] in substantial agreement with ours but is still in conflict with the interpretation of the experimental data of ref 33. I thank Professor Schaefer for forwarding the results of his study before publication. =
-
Viscosity Dependence of Fluorescence Quantum Yields S. Sharafy and K. A. Muszkat*1
Contribution from the Department of Chemistry, the Weizmann Institute of Science, Rehovot, Israel, and the Physikalisch-Chemisches Institut der Universitat Basel, Basel, Switzerland. Received October 28, 1970 Abstract: The normally nonfluorescent m-stilbene and sterically hindered /ranr-stilbenes become strongly fluorescent in very viscous media. Thus a maximum fluorescence quantum yield ( ) of 0.75 is measured for m-stilbene in a hydrocarbon glass. The fluorescence of these compounds is a steep function of the viscosity, due to a solvent free volume (and viscosity) dependent rate constant for the internal conversion (Si —> So) process. This dependence is traced to the effect of enhanced solvent viscosity in reducing the probability and amplitude of the twisting and on viscosity is out-of-plane-bending modes about the central double bond. The theoretical dependence of developed along the lines of the free volume theory of viscosity and is obeyed accurately by the experimental results. An uncoupling of fluorescence and intersystem crossing at high viscosities is observed for zrans-p-bromostilbene and for /ra«.r-hexamethylstilbene. The photochemical significance of this uncoupling is examined.
quantum yields of the trans to cis photoisomerstilbenes were recently found to depend very strongly on the viscosity of the medium.2 The effect was shown to be due to a solvent free volume dependent intramolecular rearrangement process subT2 or Si -* Ti intersystem sequent to the Si crossings,2-4 and the theory2 for a process of this type
The ization, 0t, of planar
(1) The Weizmann Institute, (2) D. Gegiou, K. A. Muszkat, and E, Fischer, J. Amer. Chem. Soc., 90, 12 (1968). (3) K. A. Muszkat, D. Gegiou, and E. Fischer, ibid., 89, 4814 (1967). (4) D. Gegiou, K. A. Muszkat, and E. Fischer, ibid., 90, 3907 (1968),
was developed along the lines of the free volume theory of the viscosity of liquids.5 In the present paper we wish to describe the results of an investigation of the dependence of the fluorescence quantum yields 0F on the viscosity in a number of nonpolar aromatic compounds.6 We have observed a (5) (a) . H. Cohen and D. Turnbull, J. Chem.Phys., 31,1164(1959); (b) D. B. Davies and A. J. Matheson, ibid., 45, 1000 (1966). in the (6) Other investigators have observed effects of viscosity on following systems: (a) diphenylmethane dyes, G. Oster and Y. Nishijima, J. Amer. Chem. Soc., 78, 1581 (1956); (b) tetraphenylbutadienes, M. A. El-Bayoumi and F. M. Abdel-Halim, J. Chem. Phys., 48, 2536
Sharafy, Muszkat / Viscosity Dependence
of Fluorescence
Quantum Yields
4120 ©
©H
©
©H
)©-/ /a a\ ©
%
©
©
©
6
P
Figure 2. Schematic description of the twisting (r) and out-of-plane bending (ß) vibration modes of stilbenes.
of the experimental
values10·11 using the
Litovitz12
log
=
empirical equation of
A + B/T8
(1)
which represents very accurately the experimental behavior for glycerol12 and for MCH-MCP (Figure 1) for viscosities up to 10° cP.
Temperature dependence of the viscosity of MCH/MCP
Figure (1:1) plotted according to eq 1.
1.
on the viscosity only in stilstrong dependence of benes, and for these compounds we treat the effect in terms of the theory of free volume controlled monomolecular processes. The study of viscosity dependent photochemical processes has important mechanistic implications if two concurrent processes show independent behavior. This is the case for fluorescence and trans to cis photoisomerization in several stilbenes, and the conclusions to be drawn from this research will be
In the present paper the solute molecules will be denoted as follows: I, rrmiy-stilbene; II, 3,3',5,5'-tranr-tetramethylstilbene; III, m-stilbene; IV, traiu-a-methylstilbene; V, trans-a,a '-dimethylstilbene; V', cis-a.a'-dimethylstilbene; VI, trans-2,4,6trimethylstilbene; Vil, tra/i.s-2,4,6,2',4',6'-hexamethylstilbene; VII', cis isomer of VII; VIII, triphenylethylene; IX, tetraphenylethylene; X, diphenylcyclopentene; XI, diphenylcyclobutene; and XII, rra/«-4-bromostilbene. Typical fluorescence and absorption spectra
Ph
discussed.
Most of the experimental details are described in the previous publications.2·4·7 1,2-Diphenylcyclobutene was obtained from Dr. DeBoer.8 A considerably purer grade of glycerol (Matheson Coleman and Bell, Spectroquality, anhydrous) was used in the present study. crs-Stilbene was purified by fractional distillation The purity of the compounds was checked by gas in vacuo. chromatography. The solutions in glycerol were prepared by a 100-fold dilution with glycerol of stock solutions in ethanol. Control experiments indicate that this amount of ethanol does not
affect the viscosity nor the results to any significant extent. The solutions were degassed in vacuo. For this study we have used two fluorescence standards. p-Terphenyl, ' /7Xl^.A-KX
-fluorescence
IC
-
\ x
'xi_l
So
trans
Figure 6.
Figure 5. Dependence of fluorescence quantum yields of c/s-stilbene on viscosity and temperature. Points denoted with · refer to solutions in ethanol + 6.6% water, while X indicates results for «-propyl alcohol solutions. Temperatures (in °K) are indicated for each point.
and II in glycerol are higher than in MCH-MCP. The results for low-viscosity solvents indicate that fluorescence in this group is intrinsically dependent on temperature (i.e., in addition to any dependence on viscosity). The temperature dependence of the fluorescence of unhindered stilbenes,2·4·13 will be reexamined in the present study. (b) Sterically Hindered Compounds. Figures 3 a, 4a, and 4b show that III or (nzrcs-stilbenes substituted at any of the a,a,'; 2,6,2'; or 6' positions are completely nonfiuorescent at low viscosities (i.e., down to ca. 170°K in MCH-MCP). The fluorescence observed in glycerol solutions of these compounds is thus due entirely to enhanced viscosity. An obvious problem that arises in the present context is whether the high values in MCH-MCP are due to the low temperatures, to the high viscosities prevailing at these temperatures, or to both factors combined. The solution to this problem is suggested by the results of a comparative study of the fluorescence of III in two alcoholic solvents of different viscosities (Figure 5). Ethanol + 6.6% water10 (E) was chosen as the fluid solvent and npropyl alcohol10·24 (P) as the viscous solvent. These results indicate that for any given temperature is larger in the more viscous solvent. Thus at 123, 113, and 103°K the ratios are equal respectively to / 3.9, 2.7, and 2. Very similar results were obtained when comparing solutions of m-stilbene in 3-methylpentane (3-MP) and in a mixture of 3-MP and MCH 0.40 in 3-MP at 91°K and in (1:20). Thus MCH-3-MP at 102°K. The viscosity of these two solvent systems at the above temperatures is about 107— 10® cP.24 These results indicate that high viscosity is the most important factor over this temperature range. However, some temperature dependence is also evident. Obviously, this reasoning is based on the assumption that, apart from different viscosities, these two solvent pairs would show similar specific effects, if any, due to their chemical similarity. The two cis isomers of the hindered compounds V and VII were also studied. Their fluorescence spectra are =
(24) A. C. Ling and J. E. Willard, J. Phys. Chem., 72, 1918, 3349 (1968).
Journal
of the
Jablonski-type scheme for the stilbene system.
red shifted in comparison with those of the trans isomers, and the quantum yields are very low, so that emission is discernible only at very low temperatures and high viscosities. Analysis of the Temperature Dependent Fluorescence in Planar Zrans-Stilbenes. The experimental data on which is based the schematic description (Figure 6) of the different processes in the stilbene system have been described previously.2-4 Further information about two radiationless processes of the singlet excited trans form is made available by the following analysis of the tem(in I and II) at low viscosiperature dependence of ties in MCH-MCP. We assume that at low viscosities the temperature deis due to the presence of the pendent behavior of intersystem crossing process Si -*· T2 (ISC) which requires an activation energy (£a) of a few kilocalories per mole. In the previous study a value of ¿sa = 1-4 kcal/ mol was obtained from the temperature dependence of The radiationless processes which compete with 200°K. At lower temperatures the function /( ° ) kISC' or even kIC > kiScchanges less, as then kIC This is observed at T < 200°K. The activation energy values for ISC (in the linear part of Figure 7) are 4.1 3 kcal/mol from the temkcal/mol for I (cf. with £a of and 3.8 kcal/mol for II. t4) perature dependence of . We of the Viscosity Dependence Analysis limit our treatment to the cw-stilbenes and the sterically hindered t/wis-stilbenes. These molecules have nonplanar ground states,23 and intersystem crossing is independent of the viscosity and of the temperature. This is inferred from the behavior of t (for the trans isomers) and of c (for the cis isomers).2-4 As in these is not, we conclude compounds ISC is constant but that at high viscosities intersystem crossing (ISC*) proceeds from a higher energy singlet state (Si*, cf. Figure 6). This state is converted into the Si state by the internal conversion process IC*. Stegemeyer has recently reported that high-viscosity solvents freeze down the molecular relaxation processes in III, VIII, IX, and in similar compounds.14 Therefore, final states having geometries similar to that of the initial states (FranckCondon states) are obtained either on emission or on absorption in high-viscosity solvents. These observations lead us to conclude that the Si* state is a FranckCondon state with a nuclear configuration similar to that of the ground state. From these considerations we conclude that at any temperature and viscosity —
~
=
+ 0isc* +
(6)
1
—
For any solvent the limiting fluorescence quantum yield, assume
°,
is achieved at the highest viscosities. 0. Then IC
We
that then
°
=
(7)
~~
and
0
)
~
=
/
=
kp/kjc
(8)
We limit our treatment to cases where the fluoresis determined by the viscosity. IC is the process whose rate constant klc is viscosity dependent. According to a previous publication2 the dependence of kIC on the mean free volume of the solvent, V{, is given by cence
kic
klc°e-aV°/Vl
=
(9)
Ineq9kiC° is the free volume independent rate constant, V/Vi
(10)
Thus kIC may be expressed in terms of the viscosity
k,c
=
klc°(volv)a
as
(ID
Figure 7. Plot of 0f/(0f° ) vs. 1/Ffor rra/zs-stilbene and transtetramethylstilbene (MCH-IH solutions). —
Substitution for kIC in eq
0
)
~
8 =
results in
kp/lkic°(Volv)a]
(12)
The absorption spectra of the present compounds are independent of the viscosity. Thus kP as well as kp/(kic°’7oa) are constant. kP/(kIc0t)o0) will be denoted by A. Our final expression is then
0
~
)
~
/
(12a)
show the linear dependence of log for III, IV, V, VI, VIII, IX, and X, as required by eq 12a. The slope of the curves, a, is larger for MCH-MCP than for glycerol. Thus for IX a is in gena is 1 in MCH-MCP but 0.2 in glycerol, eral a function both of the solvent and of the solute. Correlation between the Theory of Radiationless Transitions and the Viscosity Dependence of P. We have shown in the previous sections that the molecular are the motions which have a direct influence on twisting (t) and the out-of-plane bending (ß) motions of the a~a' double bond, in the excited state. The process whose rate constant depends on the viscosity (and on and 8) was furthermore identified as the IC radiationless transition. In the present section we wish to examine the reasons for the strong effect of these vibrations on the rate constant of the IC transition. Of the many theories of radiationless transitions,26 we chose for the present discussion the well-known formulation of Robinson and Frosch.273 According to this theory, the rate constant k for a radiationless transition (kiC in the present case) is given by
Figures 8, 9, and
[ /( °
—
)]
k
on
=
10
log
(2 ^.2 ) ( ,7 ,>2
(13)
In this equation the summation represents the overall (26) (a( B. R. Henry and M. Kasha, Annu. Rev. Phys. Chem., 19, (1968); (b) J. Jortner, S. A. Rice, and R. M. Hochstrasser, Ativan. Photochem., 7, 149 (1969). (27) (a) G. W. Robinson and R. P. Frosch, J. Chem. Phys., 37, 1962 (1962); 38, 1187 (1963); (b) W. Siebrand and D. F. Williams, ibid., 49, 1860 (1968), and literature cited therein. 161
Sharafy, Muszkat / Viscosity Dependence
of Fluorescence
Quantum Yields
4124
Figures 8 (left), 9 (center), and 10 (right). Plots of denoted with Roman numerals (see Experimental Section).
Figure bene.
form.
·0
—
Schematic energy profiles for the twisting mode of stilCurve d refers to a molar volume equal to that of the trans 11.
vibrational overlap factor (Franck-Condon factor),
is the matrix element of the electronic perturbation Hamiltonian H' between the final and initial wave functions, and a is an inverse measure of the density of final states. In the present discussion we shall be mainly concerned with the Franck-Condon (FC) factor of eq 13. This factor accounts for overlap of the lowest vibrational wave function of the higher electronic state a single prime), 0', with all the n functions of the lower electronic state (designated by a double prime), ". Siebrand and Williams have recently investigated several of the factors which strongly increase the magnitude of FC factors for the Sj — S0 internal conversion.276 Among these factors are included the anharmonicity of the excited vibrations in the lower electronic state, the extent of change in the frequencies of the excited modes between the two states (distortions), and the extent of change in the normal coordinates proper to the excited normal modes (displacements).276 Low-frequency modes are expected to be particularly effective.276 All these requirements are obviously fulfilled by the r mode28 and probably by the out-of-
(designated by
different
wave
(28) A. J. Merer and R. S. Mulliken, Chem. Rev., 69, 639 (1969).
Journal
of the
)
The solvents
on are
logarithmic scale
vs.
log (viscosity).
The compounds are
MCH-MCP (1) and glycerol (2).
plane-bending modes. However, this approach is unable to explain why modes r and ß are of particular importance for the nonplanar molecules. It seems that for these other factors have also to be considered. The experimental data of Auwers29 on the molar volumes of sterically nonhindered (planar) and sterically hindered (nonplanar) isomers in solution point toward the general trend that planar molecules have smaller molar volumes than nonplanar molecules. We have therefore attributed the difference in the viscosity dependence of the quantum yields of geometrical photoisomerization between planar /ra/i-y-stilbenes and the nonplanar cis- or ira«5-stilbenes to a difference in the molar volumes.2 According to this approach2 the combined molecular volume of the solute and the mean free volume of the solvent are sufficient at all viscosities for the rotation about the central double bond in the nonplanar compounds. However, in the planar compounds this motion mode is probable only at low viscosities (i.e., at high values of the solvent mean free volume). Thus at intermediate viscosities the probability of the twisting motion in a triplet state and therefore the photoisomerization quantum yield should show a dependence on the viscosity. This same approach provides an immediate explanation of the present experimental results. In the previous sections we have seen that the motions involving the double bond (r and the /3’s) are closely related to the magnitude of IC and to its dependence on the viscosity. We therefore wish to suggest that an important path for internal conversion in stilbenes is through tunneling of molecules twisted by 90° about the central double bond in Si (Figure 11) to the perpendicular ground state. Figure 11 gives a qualitative description of the energy profiles of several electronic states important for the present context as a function of the angle of twist of the central double bond.30'31 The lowest energy (29) K. v. Auwers, Chem, Ber., 68B, 1346 (1935).
American Chemical Society / 93 :17 / August 25, 1971
4125
gap Si-So is between the perpendicular forms, and a radiationless transition Si -* S0 would be the most probable
for this geometry. Curve c describes the energy of the Si state at low viscosities. However, at high viscosities, depending
on
the solute and
on
the viscosity,
a
poten-
tial barrier of varying height which is required for a free volume limited motion will be superimposed on the potential curve of the Si state of the isolated molecule Therefore, planar (rans-stilbenes which have low molar volumes will experience high viscosity demotion and will show a dependent barriers to the crease of 0ic even at relatively low viscosities (Figure 3b). The nonplanar stilbenes which have higher molar volumes will show a decrease of 0IC only at much higher viscosities because they experience much lower free volume dependent barriers to rotations. The present approach can also be applied to another chapter of the photochemistry of stilbene. Herkstroeter and McClure have observed that the lifetime of the triplet state of ¿ranó-stilbene is very strongly dependent on viscosity.25 On the other hand, it is considerably increased by deuteration, but only at the a and a' positions (I).32 These two observations can easily be correlated by assuming that a preferred path for the radiationless transition Ti -*· S0 (trans) which determines the lifetime of the triplet also involves a twisted or bent upper state. This state is converted to the isoenergetic lower state excited with one or several of the outof-plane vibrations involving the double bond. These correspond respectively to the modes ve (au), (au), and The transition Ti -* S0 is, p8 (bg) of CHBr=CHBr.19 a surface not however, simple crossing but also requires The frequencies some quantum mechanical tunneling. of the out-of-plane bending vibrations au and bg are probably strongly decreased by deuteration at a and a' (cf. the effect in CHBr=CHBr19), while in the V state of ethylene deuteration is known to reduce considerably the frequency of the double bond twisting mode.33 Energy profiles qualitatively similar to that for the twisting deformation (Figure 11) are also expected for the out-of-plane-bending modes. (curve d).
(30) P. Borrell and . 453 (1967).
H. Greenwood, Proc. Roy. Soc., Ser. A, 298,
MO calculation (31) Cf. the diagram based on the semiempirical 5 in ref 30) and the analogous situation in ethylene (Figure 3 of
(Figure ref 28).
(32) G. Heinrich, G. Holzer, H. Blume, and D. Schulte-Frohlinde, Z. Naturforsch. B, 25, 496 (1970). (33) R. McDiarmid and E, Charney, J, Chem. Phys., 47, 1517 (1967).
The two effects on the lifetime of the triplet state of stilbene—that of viscosity and that of deuteration at the a and a' positions—are thus ascribed to the participation of the twisting and of the out-of-plane-bending modes in the radiationless Ti S0 transition. Conclusion about the Mechanism of the Direct CisTrans Photoisomerization of Stilbenes. The involvement of triplet levels in the direct photoisomerization of stilbenes has been a subject of controversy.2""4·13'22'25'34 Mainly on the basis of quenching experiments of the sensitized and of the direct photoisomerization of stilbene, Saltiel, etal., infer34 that the unsensitized photoisomerization proceeds in an excited singlet level. However, studies of triplet sensitization 13·35 and of the effects of internal and external heavyatom enhancement2-4·36 on Si Ti and on S0 -* Ti indicate that a triplet level is involved which may be directly observed by triplet-triplet absorption in flash photolysis.25 The present investigation supports this last conclusion: the effects of high viscosity on 0F and on 0t values in VI and XII show that there is complete uncoupling of fluorescence and trans-to-cis photoisomerization in both VII and XII,37 as well as in III, IV, V, and VI. Thus in VI 0t is independent both of temperature and of viscosity2·4 while 0F is strongly dependent on the viscosity and to a lesser degree on the temperature (Figure 3). In XII in glycerol solutions at 80° 0t is decreased to almost zero while 0F is approximately equal to its value at this temperature in the fluid MCH-MCP (cf Figure 3). Acknowledgments. K. A. M. wishes to thank Professor E. Heilbronner for his hospitality at the Physikalisch-Chemisches Instituí der Universitat Basel and the Bank J. Bar and Co. (Zürich) for support. Both authors are indebted to Professor E. Fischer for many discussions and for his interest in this work. —
(34) (a) J. Saltiel, J. Amer. Chem. Soc., 89, 1037 (1967); 90, 6394 (1968); (b) J. Saltiel, E. D. Megarity, and K. G. Kneipp, ibid., 88, 2336 (1966); (c) J. Saltiel, O. C. Zafiriou, E. D. Megarity, and A. A. Lamola, ibid., 90, 4759 (1968). (35) (a) G. S. Hammond, et al., ibid., 86, 3197 (1964); (b) G. S. Hammond and J. Saltiel, ibid,, 84, 4984 (1962). (36) G. Fischer, K. A. Muszkat, and E. Fischer, Israel J. Chem., 6, 965 (1968). values for rrara-stilbene (I) show that here no (37) The present experimental proof is available of uncoupling of fluorescence and of photoisomerization at high viscosities. At high viscosities, in glycerol increases (see Figure 3), implying a vissolutions, drops,2 while cosity dependent ISC process. An uncoupling of fluorescence and trans-to-cis photoisomerization at high viscosities2,5 was deduced values.2,3 For I these erroneously for I from the previous set of are superseded by the present measurements (cf. Experimental Section)
Sharafy, Muszkat / Viscosity Dependence
of Fluorescence
Quantum Yields
